Ramsey-ed!!

Level pending

Let S={1,2,3.....6} i is said to be a fixed point of a permutation p or S if p(i)=i,where i belongs to S.Let \(p_{n} (k)\) be the number of permutations of S which have k fixed points. Find \(\sum_{k=0}^n k p_{n}(k)/n \)?

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